We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein–Stein, and Hull–White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier‐transform‐based method in the nested affine cases. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.

中文翻译：

---

具有正交多项式展开式的期权定价

我们在多项式随机波动率模型中导出了欧洲期权价格的分析级数表示。这包括Jacobi，Heston，Stein–Stein和Hull–White模型，我们为它们提供了数值案例研究。我们发现，在嵌套仿射案例中，多项式期权价格序列的扩展与基于傅立叶变换的方法一样有效和准确。我们还为期权希腊人推导了序列表示并对其进行了数值验证。我们描述了一种方法的扩展，该方法适用于异国期权，其收益取决于有限数量的价格。